Answer:
The three consecutive odd natural numbers are 5, 7 and 9
Step-by-step explanation:
- Natural numbers are all positive integers from 1 to ∞
- We are given that the three numbers are consecutive odd natural numbers
- If we let the numbers be a, b and c then because consecutive odd numbers have a difference of 2 we get
a = b - 2
c = b + 2
- We are given that the sum of the squares of the numbers = 155
- That means
a² + b² + c² = 155
- Substituting in terms of b:
(b - 2)² + b² + (b + 2)² = 155
- Using the identity (a + b)² = a² + 2ab + b²
we get
(b² - 2ab + 2²) + b² + (b² + 2ab + 2²) = 155
b² - 2ab + 4 + b² + b² +2ab + 4 = 155
- Grouping like terms:
b² + b² + b² - 2ab + 2ab + 4 + 4 = 155
3b² + 8 = 155
3b² = 155 - 8
3b² = 147
b² = 147/3
b² = 49
b = √49
b = 7
Therefore a = 7 - 2 = 5 and c = 7 + 2 = 9
The three consecutive odd numbers are 5, 7 and 9
